On a different ground, in the framework of statistical mechanics based on the Tsallis entropy [1]}, the nonlinear Fourier transform [2]} defined in
\({\cal F}_q[f(x)](\omega )=\int \limits _{-\infty }\limits ^{+\infty }f(x)\otimes _q\exp _q(-i\,x\,\omega )\,dx \ ,\) 
